@techreport{NBERw1885,
title = "Cointegration and Tests of Present Value Models",
author = "John Y. Campbell and Robert J. Shiller",
institution = "National Bureau of Economic Research",
type = "Working Paper",
series = "Working Paper Series",
number = "1885",
year = "1988",
month = "June",
URL = "http://www.nber.org/papers/w1885",
abstract = {In a model where a variable Y[sub t] is proportional to the present value, with constant discount rate, of expected future values of a variable y[sub t] the "spread" S[sub t]= Y[sub t] - [theta sub t] will be stationary for some [theta] whether or not y[sub t]must be differenced to induce stationarity. Thus, Y[sub t] and y[sub t] are cointegrated. The model implies that S[sub t] is proportional to the optimal forecast of [delta Y\{sub t+1\}] and also to the optimal forecast of S*[sub t], the present value of future [delta y\{sub t\}]. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y[sub t] is the long-term interest rate and y[sub t] the short-term interest rate, we find in postwar U.S. data that S[sub t] behaves much like an optimal forecast of S*[sub t] even though as earlier research has shown it is negatively correlated with [delta Y\{sub t+1\}]. When Y[sub t] is a real stock price index and y[sub t] the corresponding real dividend, using annual U.S. data for 1871-1986 we obtain less encouraging results for the model, al-though the results are sensitive to the assumed discount rate.},
}